Properties

Label 720.3.bh.f.577.1
Level $720$
Weight $3$
Character 720.577
Analytic conductor $19.619$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [720,3,Mod(433,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.433");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 720.bh (of order \(4\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(19.6185790339\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 577.1
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 720.577
Dual form 720.3.bh.f.433.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.22474 - 2.67423i) q^{5} +(-7.44949 - 7.44949i) q^{7} +O(q^{10})\) \(q+(-4.22474 - 2.67423i) q^{5} +(-7.44949 - 7.44949i) q^{7} -16.2474 q^{11} +(12.2474 - 12.2474i) q^{13} +(7.55051 + 7.55051i) q^{17} +14.4949i q^{19} +(-2.65153 + 2.65153i) q^{23} +(10.6969 + 22.5959i) q^{25} +34.2474i q^{29} +20.4949 q^{31} +(11.5505 + 51.3939i) q^{35} +(7.34847 + 7.34847i) q^{37} -25.5051 q^{41} +(-25.1010 + 25.1010i) q^{43} +(22.0454 + 22.0454i) q^{47} +61.9898i q^{49} +(35.3031 - 35.3031i) q^{53} +(68.6413 + 43.4495i) q^{55} -88.7423i q^{59} -102.495 q^{61} +(-84.4949 + 18.9898i) q^{65} +(24.6969 + 24.6969i) q^{67} +77.9796 q^{71} +(-44.1918 + 44.1918i) q^{73} +(121.035 + 121.035i) q^{77} +48.4949i q^{79} +(-101.641 + 101.641i) q^{83} +(-11.7071 - 52.0908i) q^{85} -156.969i q^{89} -182.474 q^{91} +(38.7628 - 61.2372i) q^{95} +(55.4041 + 55.4041i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 12 q^{5} - 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 12 q^{5} - 20 q^{7} - 16 q^{11} + 40 q^{17} - 40 q^{23} - 16 q^{25} - 16 q^{31} + 56 q^{35} - 200 q^{41} - 120 q^{43} + 200 q^{53} + 108 q^{55} - 312 q^{61} - 240 q^{65} + 40 q^{67} - 80 q^{71} - 20 q^{73} + 200 q^{77} - 240 q^{83} - 184 q^{85} - 240 q^{91} + 400 q^{95} + 300 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −4.22474 2.67423i −0.844949 0.534847i
\(6\) 0 0
\(7\) −7.44949 7.44949i −1.06421 1.06421i −0.997792 0.0664211i \(-0.978842\pi\)
−0.0664211 0.997792i \(-0.521158\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −16.2474 −1.47704 −0.738520 0.674231i \(-0.764475\pi\)
−0.738520 + 0.674231i \(0.764475\pi\)
\(12\) 0 0
\(13\) 12.2474 12.2474i 0.942111 0.942111i −0.0563023 0.998414i \(-0.517931\pi\)
0.998414 + 0.0563023i \(0.0179311\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.55051 + 7.55051i 0.444148 + 0.444148i 0.893403 0.449256i \(-0.148311\pi\)
−0.449256 + 0.893403i \(0.648311\pi\)
\(18\) 0 0
\(19\) 14.4949i 0.762889i 0.924392 + 0.381445i \(0.124573\pi\)
−0.924392 + 0.381445i \(0.875427\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.65153 + 2.65153i −0.115284 + 0.115284i −0.762395 0.647111i \(-0.775977\pi\)
0.647111 + 0.762395i \(0.275977\pi\)
\(24\) 0 0
\(25\) 10.6969 + 22.5959i 0.427878 + 0.903837i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 34.2474i 1.18095i 0.807057 + 0.590473i \(0.201059\pi\)
−0.807057 + 0.590473i \(0.798941\pi\)
\(30\) 0 0
\(31\) 20.4949 0.661126 0.330563 0.943784i \(-0.392761\pi\)
0.330563 + 0.943784i \(0.392761\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 11.5505 + 51.3939i 0.330015 + 1.46840i
\(36\) 0 0
\(37\) 7.34847 + 7.34847i 0.198607 + 0.198607i 0.799403 0.600795i \(-0.205149\pi\)
−0.600795 + 0.799403i \(0.705149\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −25.5051 −0.622076 −0.311038 0.950398i \(-0.600677\pi\)
−0.311038 + 0.950398i \(0.600677\pi\)
\(42\) 0 0
\(43\) −25.1010 + 25.1010i −0.583745 + 0.583745i −0.935930 0.352186i \(-0.885439\pi\)
0.352186 + 0.935930i \(0.385439\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 22.0454 + 22.0454i 0.469051 + 0.469051i 0.901607 0.432556i \(-0.142388\pi\)
−0.432556 + 0.901607i \(0.642388\pi\)
\(48\) 0 0
\(49\) 61.9898i 1.26510i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 35.3031 35.3031i 0.666096 0.666096i −0.290714 0.956810i \(-0.593893\pi\)
0.956810 + 0.290714i \(0.0938929\pi\)
\(54\) 0 0
\(55\) 68.6413 + 43.4495i 1.24802 + 0.789991i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 88.7423i 1.50411i −0.659102 0.752054i \(-0.729063\pi\)
0.659102 0.752054i \(-0.270937\pi\)
\(60\) 0 0
\(61\) −102.495 −1.68024 −0.840122 0.542397i \(-0.817517\pi\)
−0.840122 + 0.542397i \(0.817517\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −84.4949 + 18.9898i −1.29992 + 0.292151i
\(66\) 0 0
\(67\) 24.6969 + 24.6969i 0.368611 + 0.368611i 0.866970 0.498359i \(-0.166064\pi\)
−0.498359 + 0.866970i \(0.666064\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 77.9796 1.09830 0.549152 0.835722i \(-0.314951\pi\)
0.549152 + 0.835722i \(0.314951\pi\)
\(72\) 0 0
\(73\) −44.1918 + 44.1918i −0.605368 + 0.605368i −0.941732 0.336364i \(-0.890803\pi\)
0.336364 + 0.941732i \(0.390803\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 121.035 + 121.035i 1.57189 + 1.57189i
\(78\) 0 0
\(79\) 48.4949i 0.613859i 0.951732 + 0.306930i \(0.0993017\pi\)
−0.951732 + 0.306930i \(0.900698\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −101.641 + 101.641i −1.22459 + 1.22459i −0.258613 + 0.965981i \(0.583266\pi\)
−0.965981 + 0.258613i \(0.916734\pi\)
\(84\) 0 0
\(85\) −11.7071 52.0908i −0.137731 0.612833i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 156.969i 1.76370i −0.471529 0.881850i \(-0.656298\pi\)
0.471529 0.881850i \(-0.343702\pi\)
\(90\) 0 0
\(91\) −182.474 −2.00521
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 38.7628 61.2372i 0.408029 0.644603i
\(96\) 0 0
\(97\) 55.4041 + 55.4041i 0.571176 + 0.571176i 0.932457 0.361281i \(-0.117660\pi\)
−0.361281 + 0.932457i \(0.617660\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −45.7526 −0.452996 −0.226498 0.974012i \(-0.572728\pi\)
−0.226498 + 0.974012i \(0.572728\pi\)
\(102\) 0 0
\(103\) −23.1566 + 23.1566i −0.224822 + 0.224822i −0.810525 0.585704i \(-0.800818\pi\)
0.585704 + 0.810525i \(0.300818\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.3383 + 16.3383i 0.152694 + 0.152694i 0.779320 0.626626i \(-0.215565\pi\)
−0.626626 + 0.779320i \(0.715565\pi\)
\(108\) 0 0
\(109\) 159.485i 1.46316i 0.681754 + 0.731581i \(0.261217\pi\)
−0.681754 + 0.731581i \(0.738783\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −13.0556 + 13.0556i −0.115536 + 0.115536i −0.762511 0.646975i \(-0.776034\pi\)
0.646975 + 0.762511i \(0.276034\pi\)
\(114\) 0 0
\(115\) 18.2929 4.11123i 0.159068 0.0357498i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 112.495i 0.945335i
\(120\) 0 0
\(121\) 142.980 1.18165
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 15.2350 124.068i 0.121880 0.992545i
\(126\) 0 0
\(127\) −7.44949 7.44949i −0.0586574 0.0586574i 0.677170 0.735827i \(-0.263206\pi\)
−0.735827 + 0.677170i \(0.763206\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 19.7526 0.150783 0.0753914 0.997154i \(-0.475979\pi\)
0.0753914 + 0.997154i \(0.475979\pi\)
\(132\) 0 0
\(133\) 107.980 107.980i 0.811877 0.811877i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 101.641 + 101.641i 0.741907 + 0.741907i 0.972945 0.231037i \(-0.0742120\pi\)
−0.231037 + 0.972945i \(0.574212\pi\)
\(138\) 0 0
\(139\) 24.0204i 0.172809i −0.996260 0.0864044i \(-0.972462\pi\)
0.996260 0.0864044i \(-0.0275377\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −198.990 + 198.990i −1.39154 + 1.39154i
\(144\) 0 0
\(145\) 91.5857 144.687i 0.631626 0.997840i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 199.732i 1.34048i 0.742143 + 0.670242i \(0.233810\pi\)
−0.742143 + 0.670242i \(0.766190\pi\)
\(150\) 0 0
\(151\) 158.990 1.05291 0.526456 0.850202i \(-0.323520\pi\)
0.526456 + 0.850202i \(0.323520\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −86.5857 54.8082i −0.558618 0.353601i
\(156\) 0 0
\(157\) −37.3485 37.3485i −0.237888 0.237888i 0.578087 0.815975i \(-0.303799\pi\)
−0.815975 + 0.578087i \(0.803799\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 39.5051 0.245373
\(162\) 0 0
\(163\) −8.98979 + 8.98979i −0.0551521 + 0.0551521i −0.734145 0.678993i \(-0.762417\pi\)
0.678993 + 0.734145i \(0.262417\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 88.3587 + 88.3587i 0.529094 + 0.529094i 0.920302 0.391208i \(-0.127943\pi\)
−0.391208 + 0.920302i \(0.627943\pi\)
\(168\) 0 0
\(169\) 131.000i 0.775148i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −170.631 + 170.631i −0.986307 + 0.986307i −0.999908 0.0136005i \(-0.995671\pi\)
0.0136005 + 0.999908i \(0.495671\pi\)
\(174\) 0 0
\(175\) 88.6413 248.015i 0.506522 1.41723i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 75.7526i 0.423199i 0.977357 + 0.211599i \(0.0678672\pi\)
−0.977357 + 0.211599i \(0.932133\pi\)
\(180\) 0 0
\(181\) −279.444 −1.54389 −0.771944 0.635690i \(-0.780716\pi\)
−0.771944 + 0.635690i \(0.780716\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −11.3939 50.6969i −0.0615885 0.274038i
\(186\) 0 0
\(187\) −122.677 122.677i −0.656024 0.656024i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −69.4847 −0.363794 −0.181897 0.983318i \(-0.558224\pi\)
−0.181897 + 0.983318i \(0.558224\pi\)
\(192\) 0 0
\(193\) −53.5857 + 53.5857i −0.277646 + 0.277646i −0.832169 0.554523i \(-0.812901\pi\)
0.554523 + 0.832169i \(0.312901\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −260.252 260.252i −1.32108 1.32108i −0.912906 0.408171i \(-0.866167\pi\)
−0.408171 0.912906i \(-0.633833\pi\)
\(198\) 0 0
\(199\) 65.0102i 0.326684i 0.986569 + 0.163342i \(0.0522275\pi\)
−0.986569 + 0.163342i \(0.947773\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 255.126 255.126i 1.25678 1.25678i
\(204\) 0 0
\(205\) 107.753 + 68.2066i 0.525622 + 0.332715i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 235.505i 1.12682i
\(210\) 0 0
\(211\) −12.0204 −0.0569688 −0.0284844 0.999594i \(-0.509068\pi\)
−0.0284844 + 0.999594i \(0.509068\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 173.171 38.9194i 0.805448 0.181020i
\(216\) 0 0
\(217\) −152.677 152.677i −0.703578 0.703578i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 184.949 0.836873
\(222\) 0 0
\(223\) 239.722 239.722i 1.07499 1.07499i 0.0780357 0.996951i \(-0.475135\pi\)
0.996951 0.0780357i \(-0.0248648\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.02041 + 2.02041i 0.00890049 + 0.00890049i 0.711543 0.702643i \(-0.247997\pi\)
−0.702643 + 0.711543i \(0.747997\pi\)
\(228\) 0 0
\(229\) 284.969i 1.24441i −0.782855 0.622204i \(-0.786237\pi\)
0.782855 0.622204i \(-0.213763\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −151.237 + 151.237i −0.649087 + 0.649087i −0.952772 0.303685i \(-0.901783\pi\)
0.303685 + 0.952772i \(0.401783\pi\)
\(234\) 0 0
\(235\) −34.1816 152.091i −0.145454 0.647195i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 50.9694i 0.213261i −0.994299 0.106631i \(-0.965994\pi\)
0.994299 0.106631i \(-0.0340062\pi\)
\(240\) 0 0
\(241\) −32.0000 −0.132780 −0.0663900 0.997794i \(-0.521148\pi\)
−0.0663900 + 0.997794i \(0.521148\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 165.775 261.891i 0.676634 1.06894i
\(246\) 0 0
\(247\) 177.526 + 177.526i 0.718727 + 0.718727i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −373.237 −1.48700 −0.743500 0.668735i \(-0.766836\pi\)
−0.743500 + 0.668735i \(0.766836\pi\)
\(252\) 0 0
\(253\) 43.0806 43.0806i 0.170279 0.170279i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 206.136 + 206.136i 0.802086 + 0.802086i 0.983421 0.181335i \(-0.0580418\pi\)
−0.181335 + 0.983421i \(0.558042\pi\)
\(258\) 0 0
\(259\) 109.485i 0.422721i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 210.833 210.833i 0.801647 0.801647i −0.181706 0.983353i \(-0.558162\pi\)
0.983353 + 0.181706i \(0.0581619\pi\)
\(264\) 0 0
\(265\) −243.555 + 54.7378i −0.919076 + 0.206558i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 205.258i 0.763040i −0.924361 0.381520i \(-0.875401\pi\)
0.924361 0.381520i \(-0.124599\pi\)
\(270\) 0 0
\(271\) 66.0000 0.243542 0.121771 0.992558i \(-0.461143\pi\)
0.121771 + 0.992558i \(0.461143\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −173.798 367.126i −0.631993 1.33500i
\(276\) 0 0
\(277\) 148.157 + 148.157i 0.534861 + 0.534861i 0.922015 0.387154i \(-0.126542\pi\)
−0.387154 + 0.922015i \(0.626542\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −324.434 −1.15457 −0.577284 0.816543i \(-0.695887\pi\)
−0.577284 + 0.816543i \(0.695887\pi\)
\(282\) 0 0
\(283\) −304.747 + 304.747i −1.07684 + 1.07684i −0.0800537 + 0.996791i \(0.525509\pi\)
−0.996791 + 0.0800537i \(0.974491\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 190.000 + 190.000i 0.662021 + 0.662021i
\(288\) 0 0
\(289\) 174.980i 0.605466i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 145.151 145.151i 0.495396 0.495396i −0.414605 0.910001i \(-0.636080\pi\)
0.910001 + 0.414605i \(0.136080\pi\)
\(294\) 0 0
\(295\) −237.318 + 374.914i −0.804467 + 1.27089i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 64.9490i 0.217221i
\(300\) 0 0
\(301\) 373.980 1.24246
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 433.015 + 274.095i 1.41972 + 0.898673i
\(306\) 0 0
\(307\) −120.606 120.606i −0.392854 0.392854i 0.482850 0.875703i \(-0.339602\pi\)
−0.875703 + 0.482850i \(0.839602\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −18.0204 −0.0579434 −0.0289717 0.999580i \(-0.509223\pi\)
−0.0289717 + 0.999580i \(0.509223\pi\)
\(312\) 0 0
\(313\) −323.586 + 323.586i −1.03382 + 1.03382i −0.0344125 + 0.999408i \(0.510956\pi\)
−0.999408 + 0.0344125i \(0.989044\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −62.4495 62.4495i −0.197002 0.197002i 0.601712 0.798713i \(-0.294486\pi\)
−0.798713 + 0.601712i \(0.794486\pi\)
\(318\) 0 0
\(319\) 556.434i 1.74431i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −109.444 + 109.444i −0.338836 + 0.338836i
\(324\) 0 0
\(325\) 407.753 + 145.732i 1.25462 + 0.448407i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 328.454i 0.998341i
\(330\) 0 0
\(331\) −618.413 −1.86832 −0.934159 0.356857i \(-0.883848\pi\)
−0.934159 + 0.356857i \(0.883848\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −38.2929 170.384i −0.114307 0.508608i
\(336\) 0 0
\(337\) −55.4041 55.4041i −0.164404 0.164404i 0.620111 0.784514i \(-0.287088\pi\)
−0.784514 + 0.620111i \(0.787088\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −332.990 −0.976510
\(342\) 0 0
\(343\) 96.7673 96.7673i 0.282121 0.282121i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 413.081 + 413.081i 1.19043 + 1.19043i 0.976946 + 0.213488i \(0.0684826\pi\)
0.213488 + 0.976946i \(0.431517\pi\)
\(348\) 0 0
\(349\) 258.454i 0.740556i −0.928921 0.370278i \(-0.879262\pi\)
0.928921 0.370278i \(-0.120738\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 83.9138 83.9138i 0.237716 0.237716i −0.578188 0.815904i \(-0.696240\pi\)
0.815904 + 0.578188i \(0.196240\pi\)
\(354\) 0 0
\(355\) −329.444 208.536i −0.928011 0.587425i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 138.515i 0.385837i −0.981215 0.192918i \(-0.938205\pi\)
0.981215 0.192918i \(-0.0617952\pi\)
\(360\) 0 0
\(361\) 150.898 0.418000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 304.879 68.5199i 0.835284 0.187726i
\(366\) 0 0
\(367\) 408.964 + 408.964i 1.11434 + 1.11434i 0.992556 + 0.121786i \(0.0388623\pi\)
0.121786 + 0.992556i \(0.461138\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −525.980 −1.41773
\(372\) 0 0
\(373\) −143.106 + 143.106i −0.383661 + 0.383661i −0.872419 0.488758i \(-0.837450\pi\)
0.488758 + 0.872419i \(0.337450\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 419.444 + 419.444i 1.11258 + 1.11258i
\(378\) 0 0
\(379\) 194.000i 0.511873i 0.966694 + 0.255937i \(0.0823839\pi\)
−0.966694 + 0.255937i \(0.917616\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 51.4893 51.4893i 0.134437 0.134437i −0.636686 0.771123i \(-0.719695\pi\)
0.771123 + 0.636686i \(0.219695\pi\)
\(384\) 0 0
\(385\) −187.666 835.019i −0.487445 2.16888i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 35.1964i 0.0904792i 0.998976 + 0.0452396i \(0.0144051\pi\)
−0.998976 + 0.0452396i \(0.985595\pi\)
\(390\) 0 0
\(391\) −40.0408 −0.102406
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 129.687 204.879i 0.328321 0.518680i
\(396\) 0 0
\(397\) 409.267 + 409.267i 1.03090 + 1.03090i 0.999507 + 0.0313917i \(0.00999391\pi\)
0.0313917 + 0.999507i \(0.490006\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −375.898 −0.937401 −0.468701 0.883357i \(-0.655278\pi\)
−0.468701 + 0.883357i \(0.655278\pi\)
\(402\) 0 0
\(403\) 251.010 251.010i 0.622854 0.622854i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −119.394 119.394i −0.293351 0.293351i
\(408\) 0 0
\(409\) 207.959i 0.508458i 0.967144 + 0.254229i \(0.0818216\pi\)
−0.967144 + 0.254229i \(0.918178\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −661.085 + 661.085i −1.60069 + 1.60069i
\(414\) 0 0
\(415\) 701.221 157.596i 1.68969 0.379749i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 810.186i 1.93362i 0.255499 + 0.966809i \(0.417760\pi\)
−0.255499 + 0.966809i \(0.582240\pi\)
\(420\) 0 0
\(421\) −505.959 −1.20180 −0.600902 0.799323i \(-0.705192\pi\)
−0.600902 + 0.799323i \(0.705192\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −89.8434 + 251.378i −0.211396 + 0.591478i
\(426\) 0 0
\(427\) 763.535 + 763.535i 1.78814 + 1.78814i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −92.4541 −0.214511 −0.107255 0.994232i \(-0.534206\pi\)
−0.107255 + 0.994232i \(0.534206\pi\)
\(432\) 0 0
\(433\) 69.8990 69.8990i 0.161430 0.161430i −0.621770 0.783200i \(-0.713586\pi\)
0.783200 + 0.621770i \(0.213586\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −38.4337 38.4337i −0.0879489 0.0879489i
\(438\) 0 0
\(439\) 128.929i 0.293687i −0.989160 0.146843i \(-0.953089\pi\)
0.989160 0.146843i \(-0.0469114\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −335.555 + 335.555i −0.757461 + 0.757461i −0.975860 0.218399i \(-0.929917\pi\)
0.218399 + 0.975860i \(0.429917\pi\)
\(444\) 0 0
\(445\) −419.773 + 663.156i −0.943310 + 1.49024i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 521.423i 1.16130i 0.814153 + 0.580650i \(0.197201\pi\)
−0.814153 + 0.580650i \(0.802799\pi\)
\(450\) 0 0
\(451\) 414.393 0.918831
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 770.908 + 487.980i 1.69430 + 1.07248i
\(456\) 0 0
\(457\) 548.939 + 548.939i 1.20118 + 1.20118i 0.973808 + 0.227371i \(0.0730129\pi\)
0.227371 + 0.973808i \(0.426987\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −142.288 −0.308651 −0.154326 0.988020i \(-0.549320\pi\)
−0.154326 + 0.988020i \(0.549320\pi\)
\(462\) 0 0
\(463\) −537.045 + 537.045i −1.15993 + 1.15993i −0.175434 + 0.984491i \(0.556133\pi\)
−0.984491 + 0.175434i \(0.943867\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −367.044 367.044i −0.785962 0.785962i 0.194867 0.980830i \(-0.437572\pi\)
−0.980830 + 0.194867i \(0.937572\pi\)
\(468\) 0 0
\(469\) 367.959i 0.784561i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 407.828 407.828i 0.862215 0.862215i
\(474\) 0 0
\(475\) −327.526 + 155.051i −0.689527 + 0.326423i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 94.9694i 0.198266i 0.995074 + 0.0991330i \(0.0316069\pi\)
−0.995074 + 0.0991330i \(0.968393\pi\)
\(480\) 0 0
\(481\) 180.000 0.374220
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −85.9046 382.232i −0.177123 0.788106i
\(486\) 0 0
\(487\) −244.621 244.621i −0.502302 0.502302i 0.409851 0.912153i \(-0.365581\pi\)
−0.912153 + 0.409851i \(0.865581\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 163.217 0.332417 0.166209 0.986091i \(-0.446847\pi\)
0.166209 + 0.986091i \(0.446847\pi\)
\(492\) 0 0
\(493\) −258.586 + 258.586i −0.524515 + 0.524515i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −580.908 580.908i −1.16883 1.16883i
\(498\) 0 0
\(499\) 8.55613i 0.0171465i −0.999963 0.00857327i \(-0.997271\pi\)
0.999963 0.00857327i \(-0.00272899\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 46.5903 46.5903i 0.0926249 0.0926249i −0.659276 0.751901i \(-0.729137\pi\)
0.751901 + 0.659276i \(0.229137\pi\)
\(504\) 0 0
\(505\) 193.293 + 122.353i 0.382758 + 0.242283i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 336.227i 0.660564i 0.943882 + 0.330282i \(0.107144\pi\)
−0.943882 + 0.330282i \(0.892856\pi\)
\(510\) 0 0
\(511\) 658.413 1.28848
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 159.757 35.9046i 0.310208 0.0697177i
\(516\) 0 0
\(517\) −358.182 358.182i −0.692808 0.692808i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −252.556 −0.484753 −0.242376 0.970182i \(-0.577927\pi\)
−0.242376 + 0.970182i \(0.577927\pi\)
\(522\) 0 0
\(523\) 33.6867 33.6867i 0.0644106 0.0644106i −0.674168 0.738578i \(-0.735498\pi\)
0.738578 + 0.674168i \(0.235498\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 154.747 + 154.747i 0.293637 + 0.293637i
\(528\) 0 0
\(529\) 514.939i 0.973419i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −312.372 + 312.372i −0.586065 + 0.586065i
\(534\) 0 0
\(535\) −25.3326 112.717i −0.0473507 0.210687i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1007.18i 1.86860i
\(540\) 0 0
\(541\) −604.474 −1.11733 −0.558664 0.829394i \(-0.688686\pi\)
−0.558664 + 0.829394i \(0.688686\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 426.499 673.782i 0.782568 1.23630i
\(546\) 0 0
\(547\) −615.353 615.353i −1.12496 1.12496i −0.990985 0.133975i \(-0.957226\pi\)
−0.133975 0.990985i \(-0.542774\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −496.413 −0.900931
\(552\) 0 0
\(553\) 361.262 361.262i 0.653277 0.653277i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 439.040 + 439.040i 0.788222 + 0.788222i 0.981203 0.192980i \(-0.0618154\pi\)
−0.192980 + 0.981203i \(0.561815\pi\)
\(558\) 0 0
\(559\) 614.847i 1.09991i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −52.5765 + 52.5765i −0.0933864 + 0.0933864i −0.752257 0.658870i \(-0.771035\pi\)
0.658870 + 0.752257i \(0.271035\pi\)
\(564\) 0 0
\(565\) 90.0704 20.2429i 0.159417 0.0358281i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 680.929i 1.19671i 0.801231 + 0.598356i \(0.204179\pi\)
−0.801231 + 0.598356i \(0.795821\pi\)
\(570\) 0 0
\(571\) −254.495 −0.445700 −0.222850 0.974853i \(-0.571536\pi\)
−0.222850 + 0.974853i \(0.571536\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −88.2770 31.5505i −0.153525 0.0548705i
\(576\) 0 0
\(577\) −279.999 279.999i −0.485267 0.485267i 0.421542 0.906809i \(-0.361489\pi\)
−0.906809 + 0.421542i \(0.861489\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1514.35 2.60646
\(582\) 0 0
\(583\) −573.585 + 573.585i −0.983850 + 0.983850i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 312.347 + 312.347i 0.532108 + 0.532108i 0.921199 0.389091i \(-0.127211\pi\)
−0.389091 + 0.921199i \(0.627211\pi\)
\(588\) 0 0
\(589\) 297.071i 0.504366i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 424.570 424.570i 0.715969 0.715969i −0.251808 0.967777i \(-0.581025\pi\)
0.967777 + 0.251808i \(0.0810251\pi\)
\(594\) 0 0
\(595\) −300.838 + 475.262i −0.505610 + 0.798760i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 396.536i 0.661996i −0.943631 0.330998i \(-0.892615\pi\)
0.943631 0.330998i \(-0.107385\pi\)
\(600\) 0 0
\(601\) 238.908 0.397518 0.198759 0.980048i \(-0.436309\pi\)
0.198759 + 0.980048i \(0.436309\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −604.052 382.361i −0.998434 0.632002i
\(606\) 0 0
\(607\) −92.8025 92.8025i −0.152887 0.152887i 0.626519 0.779406i \(-0.284479\pi\)
−0.779406 + 0.626519i \(0.784479\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 540.000 0.883797
\(612\) 0 0
\(613\) 301.943 301.943i 0.492567 0.492567i −0.416547 0.909114i \(-0.636760\pi\)
0.909114 + 0.416547i \(0.136760\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 372.904 + 372.904i 0.604382 + 0.604382i 0.941472 0.337090i \(-0.109443\pi\)
−0.337090 + 0.941472i \(0.609443\pi\)
\(618\) 0 0
\(619\) 815.939i 1.31816i 0.752074 + 0.659078i \(0.229053\pi\)
−0.752074 + 0.659078i \(0.770947\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1169.34 + 1169.34i −1.87695 + 1.87695i
\(624\) 0 0
\(625\) −396.151 + 483.414i −0.633842 + 0.773463i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 110.969i 0.176422i
\(630\) 0 0
\(631\) −550.434 −0.872320 −0.436160 0.899869i \(-0.643662\pi\)
−0.436160 + 0.899869i \(0.643662\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 11.5505 + 51.3939i 0.0181898 + 0.0809352i
\(636\) 0 0
\(637\) 759.217 + 759.217i 1.19186 + 1.19186i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −927.939 −1.44764 −0.723821 0.689988i \(-0.757616\pi\)
−0.723821 + 0.689988i \(0.757616\pi\)
\(642\) 0 0
\(643\) −190.960 + 190.960i −0.296983 + 0.296983i −0.839831 0.542848i \(-0.817346\pi\)
0.542848 + 0.839831i \(0.317346\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −637.146 637.146i −0.984770 0.984770i 0.0151154 0.999886i \(-0.495188\pi\)
−0.999886 + 0.0151154i \(0.995188\pi\)
\(648\) 0 0
\(649\) 1441.84i 2.22163i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 404.116 404.116i 0.618860 0.618860i −0.326379 0.945239i \(-0.605828\pi\)
0.945239 + 0.326379i \(0.105828\pi\)
\(654\) 0 0
\(655\) −83.4495 52.8230i −0.127404 0.0806457i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 453.196i 0.687703i 0.939024 + 0.343852i \(0.111732\pi\)
−0.939024 + 0.343852i \(0.888268\pi\)
\(660\) 0 0
\(661\) 717.546 1.08555 0.542773 0.839879i \(-0.317374\pi\)
0.542773 + 0.839879i \(0.317374\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −744.949 + 167.423i −1.12022 + 0.251765i
\(666\) 0 0
\(667\) −90.8082 90.8082i −0.136144 0.136144i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1665.28 2.48179
\(672\) 0 0
\(673\) −121.413 + 121.413i −0.180406 + 0.180406i −0.791533 0.611127i \(-0.790717\pi\)
0.611127 + 0.791533i \(0.290717\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 671.943 + 671.943i 0.992531 + 0.992531i 0.999972 0.00744150i \(-0.00236873\pi\)
−0.00744150 + 0.999972i \(0.502369\pi\)
\(678\) 0 0
\(679\) 825.464i 1.21571i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 802.095 802.095i 1.17437 1.17437i 0.193214 0.981157i \(-0.438109\pi\)
0.981157 0.193214i \(-0.0618913\pi\)
\(684\) 0 0
\(685\) −157.596 701.221i −0.230067 1.02368i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 864.745i 1.25507i
\(690\) 0 0
\(691\) 1146.49 1.65918 0.829591 0.558371i \(-0.188574\pi\)
0.829591 + 0.558371i \(0.188574\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −64.2362 + 101.480i −0.0924262 + 0.146015i
\(696\) 0 0
\(697\) −192.577 192.577i −0.276293 0.276293i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 673.217 0.960366 0.480183 0.877168i \(-0.340570\pi\)
0.480183 + 0.877168i \(0.340570\pi\)
\(702\) 0 0
\(703\) −106.515 + 106.515i −0.151515 + 0.151515i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 340.833 + 340.833i 0.482084 + 0.482084i
\(708\) 0 0
\(709\) 955.939i 1.34829i −0.738598 0.674146i \(-0.764512\pi\)
0.738598 0.674146i \(-0.235488\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −54.3429 + 54.3429i −0.0762172 + 0.0762172i
\(714\) 0 0
\(715\) 1372.83 308.536i 1.92004 0.431518i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 89.0306i 0.123826i 0.998082 + 0.0619128i \(0.0197201\pi\)
−0.998082 + 0.0619128i \(0.980280\pi\)
\(720\) 0 0
\(721\) 345.010 0.478516
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −773.853 + 366.343i −1.06738 + 0.505300i
\(726\) 0 0
\(727\) −332.703 332.703i −0.457638 0.457638i 0.440242 0.897879i \(-0.354893\pi\)
−0.897879 + 0.440242i \(0.854893\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −379.051 −0.518538
\(732\) 0 0
\(733\) 229.823 229.823i 0.313537 0.313537i −0.532741 0.846278i \(-0.678838\pi\)
0.846278 + 0.532741i \(0.178838\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −401.262 401.262i −0.544454 0.544454i
\(738\) 0 0
\(739\) 923.281i 1.24936i −0.780879 0.624682i \(-0.785228\pi\)
0.780879 0.624682i \(-0.214772\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −585.782 + 585.782i −0.788401 + 0.788401i −0.981232 0.192831i \(-0.938233\pi\)
0.192831 + 0.981232i \(0.438233\pi\)
\(744\) 0 0
\(745\) 534.131 843.817i 0.716954 1.13264i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 243.423i 0.324998i
\(750\) 0 0
\(751\) −1354.27 −1.80329 −0.901645 0.432477i \(-0.857639\pi\)
−0.901645 + 0.432477i \(0.857639\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −671.691 425.176i −0.889657 0.563147i
\(756\) 0 0
\(757\) −985.832 985.832i −1.30229 1.30229i −0.926846 0.375442i \(-0.877491\pi\)
−0.375442 0.926846i \(-0.622509\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −206.495 −0.271347 −0.135673 0.990754i \(-0.543320\pi\)
−0.135673 + 0.990754i \(0.543320\pi\)
\(762\) 0 0
\(763\) 1188.08 1188.08i 1.55712 1.55712i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1086.87 1086.87i −1.41704 1.41704i
\(768\) 0 0
\(769\) 852.969i 1.10919i −0.832119 0.554596i \(-0.812873\pi\)
0.832119 0.554596i \(-0.187127\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 491.035 491.035i 0.635233 0.635233i −0.314143 0.949376i \(-0.601717\pi\)
0.949376 + 0.314143i \(0.101717\pi\)
\(774\) 0 0
\(775\) 219.233 + 463.101i 0.282881 + 0.597550i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 369.694i 0.474575i
\(780\) 0 0
\(781\) −1266.97 −1.62224
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 57.9092 + 257.666i 0.0737697 + 0.328237i
\(786\) 0 0
\(787\) 958.586 + 958.586i 1.21803 + 1.21803i 0.968323 + 0.249702i \(0.0803328\pi\)
0.249702 + 0.968323i \(0.419667\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 194.515 0.245911
\(792\) 0 0
\(793\) −1255.30 + 1255.30i −1.58298 + 1.58298i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −169.065 169.065i −0.212126 0.212126i 0.593044 0.805170i \(-0.297926\pi\)
−0.805170 + 0.593044i \(0.797926\pi\)
\(798\) 0 0
\(799\) 332.908i 0.416656i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 718.005 718.005i 0.894153 0.894153i
\(804\) 0 0
\(805\) −166.899 105.646i −0.207328 0.131237i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 126.082i 0.155849i 0.996959 + 0.0779244i \(0.0248293\pi\)
−0.996959 + 0.0779244i \(0.975171\pi\)
\(810\) 0 0
\(811\) −32.9286 −0.0406024 −0.0203012 0.999794i \(-0.506463\pi\)
−0.0203012 + 0.999794i \(0.506463\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 62.0204 13.9388i 0.0760987 0.0171028i
\(816\) 0 0
\(817\) −363.837 363.837i −0.445333 0.445333i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −980.064 −1.19374 −0.596872 0.802337i \(-0.703590\pi\)
−0.596872 + 0.802337i \(0.703590\pi\)
\(822\) 0 0
\(823\) 503.863 503.863i 0.612227 0.612227i −0.331299 0.943526i \(-0.607487\pi\)
0.943526 + 0.331299i \(0.107487\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1078.84 + 1078.84i 1.30452 + 1.30452i 0.925311 + 0.379208i \(0.123804\pi\)
0.379208 + 0.925311i \(0.376196\pi\)
\(828\) 0 0
\(829\) 124.352i 0.150002i 0.997183 + 0.0750012i \(0.0238961\pi\)
−0.997183 + 0.0750012i \(0.976104\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −468.055 + 468.055i −0.561890 + 0.561890i
\(834\) 0 0
\(835\) −137.001 609.585i −0.164073 0.730042i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1125.48i 1.34146i −0.741702 0.670730i \(-0.765981\pi\)
0.741702 0.670730i \(-0.234019\pi\)
\(840\) 0 0
\(841\) −331.888 −0.394635
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −350.325 + 553.442i −0.414585 + 0.654960i
\(846\) 0 0
\(847\) −1065.12 1065.12i −1.25753 1.25753i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −38.9694 −0.0457925
\(852\) 0 0
\(853\) 1039.87 1039.87i 1.21908 1.21908i 0.251122 0.967955i \(-0.419201\pi\)
0.967955 0.251122i \(-0.0807995\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −620.177 620.177i −0.723660 0.723660i 0.245688 0.969349i \(-0.420986\pi\)
−0.969349 + 0.245688i \(0.920986\pi\)
\(858\) 0 0
\(859\) 948.888i 1.10464i −0.833631 0.552321i \(-0.813742\pi\)
0.833631 0.552321i \(-0.186258\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1064.42 + 1064.42i −1.23339 + 1.23339i −0.270740 + 0.962652i \(0.587268\pi\)
−0.962652 + 0.270740i \(0.912732\pi\)
\(864\) 0 0
\(865\) 1177.18 264.565i 1.36090 0.305856i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 787.918i 0.906695i
\(870\) 0 0
\(871\) 604.949 0.694545
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1037.74 + 810.752i −1.18598 + 0.926573i
\(876\) 0 0
\(877\) −329.975 329.975i −0.376254 0.376254i 0.493495 0.869749i \(-0.335719\pi\)
−0.869749 + 0.493495i \(0.835719\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −135.857 −0.154208 −0.0771039 0.997023i \(-0.524567\pi\)
−0.0771039 + 0.997023i \(0.524567\pi\)
\(882\) 0 0
\(883\) 46.8694 46.8694i 0.0530797 0.0530797i −0.680069 0.733148i \(-0.738050\pi\)
0.733148 + 0.680069i \(0.238050\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −43.5097 43.5097i −0.0490526 0.0490526i 0.682155 0.731208i \(-0.261043\pi\)
−0.731208 + 0.682155i \(0.761043\pi\)
\(888\) 0 0
\(889\) 110.990i 0.124848i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −319.546 + 319.546i −0.357834 + 0.357834i
\(894\) 0 0
\(895\) 202.580 320.035i 0.226346 0.357581i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 701.898i 0.780754i
\(900\) 0 0
\(901\) 533.112 0.591690
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1180.58 + 747.298i 1.30451 + 0.825744i
\(906\) 0 0
\(907\) −638.938 638.938i −0.704452 0.704452i 0.260911 0.965363i \(-0.415977\pi\)
−0.965363 + 0.260911i \(0.915977\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 347.546 0.381499 0.190750 0.981639i \(-0.438908\pi\)
0.190750 + 0.981639i \(0.438908\pi\)
\(912\) 0 0
\(913\) 1651.41 1651.41i 1.80878 1.80878i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −147.146 147.146i −0.160465 0.160465i
\(918\) 0 0
\(919\) 27.6684i 0.0301071i −0.999887 0.0150535i \(-0.995208\pi\)
0.999887 0.0150535i \(-0.00479187\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 955.051 955.051i 1.03472 1.03472i
\(924\) 0 0
\(925\) −87.4393 + 244.652i −0.0945290 + 0.264488i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1070.49i 1.15231i −0.817341 0.576154i \(-0.804553\pi\)
0.817341 0.576154i \(-0.195447\pi\)
\(930\) 0 0
\(931\) −898.536 −0.965130
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 190.211 + 846.343i 0.203434 + 0.905180i
\(936\) 0 0
\(937\) 60.5551 + 60.5551i 0.0646266 + 0.0646266i 0.738681 0.674055i \(-0.235449\pi\)
−0.674055 + 0.738681i \(0.735449\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 264.064 0.280620 0.140310 0.990108i \(-0.455190\pi\)
0.140310 + 0.990108i \(0.455190\pi\)
\(942\) 0 0
\(943\) 67.6276 67.6276i 0.0717153 0.0717153i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −115.455 115.455i −0.121917 0.121917i 0.643516 0.765433i \(-0.277475\pi\)
−0.765433 + 0.643516i \(0.777475\pi\)
\(948\) 0 0
\(949\) 1082.47i 1.14065i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 378.359 378.359i 0.397019 0.397019i −0.480162 0.877180i \(-0.659422\pi\)
0.877180 + 0.480162i \(0.159422\pi\)
\(954\) 0 0
\(955\) 293.555 + 185.818i 0.307388 + 0.194574i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1514.35i 1.57909i
\(960\) 0 0
\(961\) −540.959 −0.562913
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 369.687 83.0852i 0.383095 0.0860987i
\(966\) 0 0
\(967\) 52.1964 + 52.1964i 0.0539777 + 0.0539777i 0.733580 0.679603i \(-0.237848\pi\)
−0.679603 + 0.733580i \(0.737848\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1545.61 −1.59177 −0.795886 0.605447i \(-0.792994\pi\)
−0.795886 + 0.605447i \(0.792994\pi\)
\(972\) 0 0
\(973\) −178.940 + 178.940i −0.183905 + 0.183905i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 843.206 + 843.206i 0.863056 + 0.863056i 0.991692 0.128636i \(-0.0410599\pi\)
−0.128636 + 0.991692i \(0.541060\pi\)
\(978\) 0 0
\(979\) 2550.35i 2.60506i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1241.39 1241.39i 1.26286 1.26286i 0.313153 0.949703i \(-0.398615\pi\)
0.949703 0.313153i \(-0.101385\pi\)
\(984\) 0 0
\(985\) 403.523 + 1795.47i 0.409668 + 1.82282i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 133.112i 0.134593i
\(990\) 0 0
\(991\) −219.816 −0.221813 −0.110906 0.993831i \(-0.535375\pi\)
−0.110906 + 0.993831i \(0.535375\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 173.853 274.652i 0.174726 0.276032i
\(996\) 0 0
\(997\) 599.571 + 599.571i 0.601375 + 0.601375i 0.940677 0.339302i \(-0.110191\pi\)
−0.339302 + 0.940677i \(0.610191\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 720.3.bh.f.577.1 4
3.2 odd 2 240.3.bg.d.97.2 4
4.3 odd 2 180.3.l.b.37.1 4
5.3 odd 4 inner 720.3.bh.f.433.1 4
12.11 even 2 60.3.k.a.37.1 yes 4
15.2 even 4 1200.3.bg.o.193.1 4
15.8 even 4 240.3.bg.d.193.2 4
15.14 odd 2 1200.3.bg.o.1057.1 4
20.3 even 4 180.3.l.b.73.1 4
20.7 even 4 900.3.l.b.793.1 4
20.19 odd 2 900.3.l.b.757.1 4
24.5 odd 2 960.3.bg.a.577.1 4
24.11 even 2 960.3.bg.b.577.2 4
60.23 odd 4 60.3.k.a.13.1 4
60.47 odd 4 300.3.k.a.193.2 4
60.59 even 2 300.3.k.a.157.2 4
120.53 even 4 960.3.bg.a.193.1 4
120.83 odd 4 960.3.bg.b.193.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.3.k.a.13.1 4 60.23 odd 4
60.3.k.a.37.1 yes 4 12.11 even 2
180.3.l.b.37.1 4 4.3 odd 2
180.3.l.b.73.1 4 20.3 even 4
240.3.bg.d.97.2 4 3.2 odd 2
240.3.bg.d.193.2 4 15.8 even 4
300.3.k.a.157.2 4 60.59 even 2
300.3.k.a.193.2 4 60.47 odd 4
720.3.bh.f.433.1 4 5.3 odd 4 inner
720.3.bh.f.577.1 4 1.1 even 1 trivial
900.3.l.b.757.1 4 20.19 odd 2
900.3.l.b.793.1 4 20.7 even 4
960.3.bg.a.193.1 4 120.53 even 4
960.3.bg.a.577.1 4 24.5 odd 2
960.3.bg.b.193.2 4 120.83 odd 4
960.3.bg.b.577.2 4 24.11 even 2
1200.3.bg.o.193.1 4 15.2 even 4
1200.3.bg.o.1057.1 4 15.14 odd 2